A366275 - OEIS

A366275

The Cat's tongue permutation: a(n) = A163511(A057889(n)).

1, 2, 4, 3, 8, 9, 6, 5, 16, 27, 18, 15, 12, 25, 10, 7, 32, 81, 54, 45, 36, 75, 30, 21, 24, 125, 50, 35, 20, 49, 14, 11, 64, 243, 162, 135, 108, 225, 90, 63, 72, 375, 150, 105, 60, 147, 42, 33, 48, 625, 250, 175, 100, 245, 70, 55, 40, 343, 98, 77, 28, 121, 22, 13, 128, 729, 486, 405, 324, 675, 270, 189, 216, 1125

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

"Cat's tongue" refers to the look of the scatter plot of this sequence.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..16383

Index entries for sequences related to binary expansion of n

Index entries for sequences that are permutations of the natural numbers

FORMULA

For n >= 0, A001222(a(n)) = A290251(n).

For n >= 1, A007814(a(n)) = A135523(n) = A007814(n) + A209229(n). [Like A163511, also this permutation preserves the 2-adic valuation of n, except when n is a power of two, in which cases that value is incremented by one.]

For n >= 1, a(2*n) = 2*a(n).

For n >= 1, a(A000225(n)) = A000040(n).

PROG

(PARI)

A030101(n) = if(n<1, 0, subst(Polrev(binary(n)), x, 2));

A057889(n) = if(!n, n, A030101(n/(2^valuation(n, 2))) * (2^valuation(n, 2)));

A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));

A366275(n) = A163511(A057889(n));

(Python)

from sympy import prime

def A366275(n):

if n:

k, c, m = int(bin(n>>(r:=(~n & n-1).bit_length()))[:1:-1], 2)<<r, 0, 1

while k:

c += 1

m *= prime(c)**(s:=(~k&k-1).bit_length())

k >>= s+1

return m*prime(c)

return 1 # Chai Wah Wu, Oct 08 2023

CROSSREFS

Cf. A000040, A000225, A007814, A057889, A163511, A209229, A290251, A366276 (inverse map), A366277 (fixed points of map n -> a(n)), A366278, A366279, A366280, A366281 [= A052409(a(n))], A366282 [= a(n)-n], A366283 [= gcd(n,a(n))].

Cf. also A163511, A253563, A366263 (compare the scatter plots).

Sequence in context: A182944 A269385 A252755 * A163511 A332817 A332214

Adjacent sequences: A366272 A366273 A366274 * A366276 A366277 A366278

KEYWORD

nonn,look

AUTHOR

Antti Karttunen, Oct 06 2023

STATUS

approved